Accounting for dimensional differences in stochastic domain invasion with applications to precancerous cell removal

Abstract

We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, stochastically simulated populations invade with a dimension dependent wave speed that can be over twice as fast as their deterministic analogues. Although the wave speed can be analytically derived in the cases of small domains, the probabilistic state space grows exponentially and, thus, we use numeric simulation and curve fitting to predict limiting dynamics.

Keywords: Agent-based modelling; Comparing deterministic and stochastic modelling; Data fitting; Eden model; Elimination; Fisher wave; Homeostasis; Juxtacrine; Pancreatic cancer; Stochastic system; Wave speed.